91Ó°ÊÓ

Perform the indicated operations. $$ \left(6 a^{2} x^{3}-2 a x^{2}+3 a^{3}\right)+\left(-4 a^{2} x^{3}-2 a^{3}\right) $$

Perform the operations and simplify the result when possible. Be careful to apply the correct method, because these problems involve addition, subtraction, multiplication, and division of rational expressions. $$\frac{x+3}{2 x^{2}-5 x+2}-\frac{3 x-1}{x^{2}-x-2}$$

Perform each operation. $$ \left(3 c^{2}+5 c\right)+\left(7-c^{2}-5 c\right) $$

Perform the operations and simplify the result when possible. Be careful to apply the correct method, because these problems involve addition, subtraction, multiplication, and division of rational expressions. $$\begin{aligned}&\text { Let } f(x)=\frac{3 x}{x^{2}-25} \text { and } g(x)=\frac{4}{x+5}\\\ &\text { Find } f(x)+g(x)\end{aligned}$$

Perform each operation. $$ -3 m n^{2}\left(m^{3}-7 m n-2 m^{2}\right) $$

Let \(f(x)=\frac{x^{3}-3 x^{2}+12}{x} .\) For what values of \(x\) is \(f(x)=4 ?\)

Perform the indicated operations. $$ (3 y+1)\left(2 y^{2}+3 y+2\right) $$

Let \(f(x)=\frac{x^{3}+2 x^{2}-32}{x} .\) For what values of \(x\) is \(f(x)=16 ?\)

Perform the operations and simplify the result when possible. Be careful to apply the correct method, because these problems involve addition, subtraction, multiplication, and division of rational expressions. $$\begin{aligned}&\text { Let } f(x)=\frac{5}{2 x-4} \text { and } g(x)=\frac{3}{2-x}\\\ &\text { Find } f(x)-g(x)\end{aligned}$$

Perform the indicated operations. $$ \left(5 k-6 m^{2}\right)^{2} $$